Gung, Mog and Pok are prehistoric tribesmen planning a hunting expedition. They have different skills: Gung...

 

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Gung, Mog and Pok are prehistoric tribesmen planning a hunting expedition. They have different skills: Gung is very strong, Mog quick and agile, and Pok has great stamina. They have to decide which of them will collaborate and which (if any) are to be left to hunt independently, and how the catch is to be divided among those who collaborate. The payoffs to coalitions are shown in Table 16.16a, with the payoffs measured by the expected value of the number of antelope they can catch. Assume this is a TU game with portions of antelope serving for side payments. a) Construct a coalition function for this game, if possible. b) Determine whether the game is superadditive. c) Describe the core of this game. Would a division of the catch in the proportions 4, 1, 1 (in the order GMP) be a stable side- payment schedule? Why or why not? Would a division of the catch in the proportions 2, 2, 2 (in the order GMP) be a stable side-payment schedule? Why or why not? 410 Game Theory: A Nontechnical Introduction to the Analysis of Strategy Table 16,16a. Prehistoric Coalitions. Coalition (GMP) (GMHP) (GP)[M) (PMHG) (GI(MHP) Payoff (6) (4)(1) (3)(1) (3)(2) (2)(181) d) Determine the Shapley Value for this game. e) Is the Shapley Value an imputation in the core of the game? Gung, Mog and Pok are prehistoric tribesmen planning a hunting expedition. They have different skills: Gung is very strong, Mog quick and agile, and Pok has great stamina. They have to decide which of them will collaborate and which (if any) are to be left to hunt independently, and how the catch is to be divided among those who collaborate. The payoffs to coalitions are shown in Table 16.16a, with the payoffs measured by the expected value of the number of antelope they can catch. Assume this is a TU game with portions of antelope serving for side payments. a) Construct a coalition function for this game, if possible. b) Determine whether the game is superadditive. c) Describe the core of this game. Would a division of the catch in the proportions 4, 1, 1 (in the order GMP) be a stable side- payment schedule? Why or why not? Would a division of the catch in the proportions 2, 2, 2 (in the order GMP) be a stable side-payment schedule? Why or why not? 410 Game Theory: A Nontechnical Introduction to the Analysis of Strategy Table 16,16a. Prehistoric Coalitions. Coalition (GMP) (GMHP) (GP)[M) (PMHG) (GI(MHP) Payoff (6) (4)(1) (3)(1) (3)(2) (2)(181) d) Determine the Shapley Value for this game. e) Is the Shapley Value an imputation in the core of the game?

Answer rating: 100% (QA)

Solution a A coalition function for this game is as follows vG 6 vM 4 vP 2 vGM 7 vGP 9 vMP 5 vGMP 8 The coalition function assigns a value to each coa... View the full answer